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 Ufimsk. Mat. Zh., 2017, Volume 9, Issue 1, Pages 109–122 (Mi ufa361)

On basicity of eigenfunctions of second order discontinuous differential operator

B. T. Bilalov, T. B. Gasymov

Institute of Mathematics and Mechanics of NAS of Azerbaijan, 9, B. Vahabzade Str., AZ1141, Baku, Azerbaijan

Abstract: We consider a spectral problem for a second order discontinuous differential operator with spectral parameter in the boundary condition. We present a method for establishing the basicity of eigenfunctions for such problem. We also consider a direct expansion of a Banach space with respect to subspaces and we propose a method for constructing a basis for a space by the bases in subspaces. We also consider the cases when the bases for subspaces are isomorphic and the corresponding isomorphisms are not needed. The completeness, minimality and uniform minimality of the corresponding systems are studied. This approach has extensive applications in the spectral theory of discontinuous differential operators.

Keywords: eigenfunctions, basis, completeness, minimality, uniform minimality.

 Funding Agency Grant Number National Academy of Sciences of Azerbaijan This work was supported by the Research Program Competition launched by the National Academy of Sciences of Azerbaijan (Program: Frame theory Applications of Wavelet Analysis to Signal Processing in Seismology and Other Fields).

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English version:
Ufa Mathematical Journal, 2017, 9:1, 109–122 (PDF, 391 kB); https://doi.org/10.13108/2017-9-1-109

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UDC: 517.984.2
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Citation: B. T. Bilalov, T. B. Gasymov, “On basicity of eigenfunctions of second order discontinuous differential operator”, Ufimsk. Mat. Zh., 9:1 (2017), 109–122; Ufa Math. J., 9:1 (2017), 109–122

Citation in format AMSBIB
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This publication is cited in the following articles:
1. T. B. Gasymov, G. V. Maharramova, A. N. Jabrailova, “Spectral properties of the problem of vibration of a loaded string in Morrey type spaces”, Proc. Inst. Math. Mech., 44:1 (2018), 116–122
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